57 ideas
| 17663 | If you know what it is, investigation is pointless. If you don't, investigation is impossible [Armstrong] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 17688 | Negative facts are supervenient on positive facts, suggesting they are positive facts [Armstrong] |
| 17691 | Nothing is genuinely related to itself [Armstrong] |
| 17679 | All instances of some property are strictly identical [Armstrong] |
| 12677 | Armstrong holds that all basic properties are categorical [Armstrong, by Ellis] |
| 17666 | Actualism means that ontology cannot contain what is merely physically possible [Armstrong] |
| 17667 | Dispositions exist, but their truth-makers are actual or categorical properties [Armstrong] |
| 17687 | If everything is powers there is a vicious regress, as powers are defined by more powers [Armstrong] |
| 17678 | Universals are just the repeatable features of a world [Armstrong] |
| 17669 | Realist regularity theories of laws need universals, to pick out the same phenomena [Armstrong] |
| 17677 | Past, present and future must be equally real if universals are instantiated [Armstrong] |
| 15442 | Universals are abstractions from their particular instances [Armstrong, by Lewis] |
| 17686 | Universals are abstractions from states of affairs [Armstrong] |
| 17668 | It is likely that particulars can be individuated by unique conjunctions of properties [Armstrong] |
| 17680 | The identity of a thing with itself can be ruled out as a pseudo-property [Armstrong] |
| 17693 | The necessary/contingent distinction may need to recognise possibilities as real [Armstrong] |
| 17685 | Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong] |
| 17683 | Science suggests that the predicate 'grue' is not a genuine single universal [Armstrong] |
| 17675 | Unlike 'green', the 'grue' predicate involves a time and a change [Armstrong] |
| 17674 | The raven paradox has three disjuncts, confirmed by confirming any one of them [Armstrong] |
| 17672 | A good reason for something (the smoke) is not an explanation of it (the fire) [Armstrong] |
| 17684 | To explain observations by a regular law is to explain the observations by the observations [Armstrong] |
| 17676 | Best explanations explain the most by means of the least [Armstrong] |
| 17664 | Each subject has an appropriate level of abstraction [Armstrong] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 17692 | We can't deduce the phenomena from the One [Armstrong] |
| 17689 | Absences might be effects, but surely not causes? [Armstrong] |
| 17682 | A universe couldn't consist of mere laws [Armstrong] |
| 17662 | Science depends on laws of nature to study unobserved times and spaces [Armstrong] |
| 17690 | Oaken conditional laws, Iron universal laws, and Steel necessary laws [Armstrong, by PG] |
| 17670 | Newton's First Law refers to bodies not acted upon by a force, but there may be no such body [Armstrong] |
| 8582 | Regularities are lawful if a second-order universal unites two first-order universals [Armstrong, by Lewis] |
| 17671 | A naive regularity view says if it never occurs then it is impossible [Armstrong] |
| 17681 | The laws of nature link properties with properties [Armstrong] |
| 16246 | Rather than take necessitation between universals as primitive, just make laws primitive [Maudlin on Armstrong] |
| 9480 | Armstrong has an unclear notion of contingent necessitation, which can't necessitate anything [Bird on Armstrong] |